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Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to reveal the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a…
With inspiration from the classic study by Chi, Feltovich, and Glaser [1], we asked introductory physics students in three introductory physics classes to categorize mechanics problems based upon similarity of solutions. To evaluate the…
Significant obstacles prevent large, university-level, introductory physics courses from effectively teaching problem-solving skills. We describe our program for integrating three internet-based "teaching-while-quizzing" tools to address…
Traditional tests are not effective tools for diagnosing the content and structure of students' knowledge of physics. As a possible alternative, a set of term-association tasks (the "ConMap" tasks) was developed to probe the…
We describe student difficulties in applying the superposition principle in combination with Gauss's law. We addressed these difficulties by developing a tutorial that uses guided inquiry. Students who used this tutorial following…
A generalized view of Duality is offered as a bridge between physical sciences and the more abstract philosophical dimensions bordering on mysticism. To that end several examples of duality are first cited from from conventional physics…
Development of conceptual multiple-choice tests related to a particular physics topic is important for designing research-based learning tools to reduce the difficulties. We explore the difficulties that the advanced undergraduate and…
The process of constructing knowledge is typically taught to students by having them reproduce established results (e.g., homework problems). An alternative pedagogical strategy is to illustrate this process using an open problem, such as…
Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations…
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…
A general novel approach mapping discrete, combinatorial, graph-theoretic problems onto ``physical'' models - namely $n$ simplexes in $n-1$ dimensions - is applied to the graph equivalence problem. It is shown to solve this long standing…
Broad instructional methods like interactive engagement have been shown to be effective, but such general characterization provides little guidance on the details of how to structure the instructional materials. In this study, we seek…
Science education at all levels is currently undergoing dramatic changes to its curricula and developing assessments for these new curricula is paramount. We have used the basis of many of these new changes (scientific practices,…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a give problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem…
Even though there has been a tremendous amount of research done in how to help students learn physics, students are still coming away missing a crucial piece of the puzzle: why bother with physics? Students learn fundamental laws and how to…
In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures.…
Analogs of fundamental physical phenomena can be used in two ways. One way consists in reproducing specific aspects of classical or quantum gravity, of quantum fields in curved space or of other high-energy scenarios, on lower-energy…
We discuss the effect of administering conceptual and quantitative isomorphic problem pairs (CQIPP) back to back vs. asking students to solve only one of the problems in the CQIPP in introductory physics courses. Students who answered both…
We investigate the dynamics of how graduate students coordinate their mathematics and physics knowledge within the context of solving a homework problem for a plasma physics survey course. Students were asked to obtain the complex…